Calculator



P. DAVEY Sept. 25, 1945.

CALCULATOR Filed Sept. 19, 1941 3 Sheets-Sheet 1 f ATTORNEY Sept. 25, 1945. p, DAVEY 2,385,334

CALCULATOR Filed Sept. 19, 1941 3 Sheets-Sheet 2 :57 mmmmum J ENTOR 6 X0 KTTO RN EY f P. DAVEY CALCULATOR Sept. 25, 1945.

Filed Sept. 19, 1941 3 Sheets-Sheet 3 ifQVfglR X v 5 29 ATTORNEY Patented Sept. 25, 1945 UNITED STATES PATENT OFFICE CALCULATOR Peter Davey, White Plains, N. Y. Application September 19, 1941, Serial No. 411,467

This invention relates to mathematics, especially to directed magnitudes, such as vectors, and particularly to an arrangement for composition and resolution thereof.

A principal object of the invention is to provide an arrangement by which, by mere mechanical movements, directed magnitudes may be sub- Jected to composition and resolution and the resuit visually indicated, as an angle and a number, defining a directed magnitude.

, '5; A fundamental fact upon which the arrangement is based is that directed magnitudes, such as vectors, may be subjected to producing an algebraic sum of equivalent sines and an algebraic sum of equivalent cosine to give; as a result an equivalent sine and an equivalent cosine deflning a vector? The equivalent sines and cosines are obtained,

creating an electrical pcthe magnitude oi'a given This electrical potential may be considered as corresponding to a radius length of the vector. After creating the electric potential, '2. portion of that potential proportional to the sine value of the angle of the vector is taken as the equivalent sine, and another portion proportional to the cosine value of the angle of the vector is taken as the equivalent cosine.

These potentials are used to create currents proportional to the potentials which are operatively applied to an electrical device, such as a galvanometer. The partial potential the equivalent sine value is then applied to an indicating device, such composition by potentials is not zero.

Similarly the partial potential taken corresponding to the equivalent cosine values are then applied to a galvanometer device along with other taken corresponding to v 4 Claims. (Cl. 235-61) plied to the sine value galvanometer and another potential is applied to the cosine value galvanometer which potentials are partial potentials proportional to the equivalent sine value and cosine.value respectively of a resultant vector. The magnitude of the resultant vector is visually indicated by the value of the whole potential used. The angle'of the resultant vector is visually indicated by the value of the portion used of the whole potential.

indicated, thereby The potential, representative of the magnitude of a vector, may well be obtained by an ordinary potentiometer, so applicant prefers to provide.

mechanically so as when a potential setrived from one of the movable slides of a magni- 'such as identical cams.

tude potentiometer and the movable slider. The center other from the other point is connected to Over the angle potentiometer two sliders travel. These sliders correspond, one to a sine and the other to acosine and, in a Preferred form, are given a simple harmonic motion by any suitable means These sliders are connected, one to the sine galvanometer and the other to the cosine galvanometer and serve to transmit that portion of the potential of the magnitude potentiometer which corresponds to the 1 equivalent sine value of the angle of the vector value of the angle of and the equivalent cosine the vector. The sliders are positioned so that at the time a maximum portion of potential is taken by the sine slider to deliver to a galvanometer a minimum of potential is taken by the cosine slider, and vice versa, the cams being set angularly 9O mechanical degrees apart, the sine cam to follow the cosine cam on increase of angle.

The combination of the duplicate potentiometers, or magnitude potentiometcrs is provided for each vector to be combined and also for the resultant vector to be obtained. A potentiometer with sliders moving with simple harmonic motion, or angle potentiometer, is alsoprovided for each given vector and also for the resultant vector, although for purposes of economy, it is possible and desirable to dispense with the sliders 'for'one of such'potentiometers, as will hereinafter more fully appear. I

A single source of potential is provided. This source is connected in multiple to the terminals of each of the magnitude potentiometers considered in pairs and the eXact intermediate 'potential point of each pair of magnitude potentio'meters and the exact intermediate potential point of each of the angle potentiometers is connected together as a common potential point.

In order to prevent excessive current flow which would interfere with potential values and to prevent low resistance shunting of the galvanometers, relatively high resistances are placed in each of the connections from the harmonic'ally moving sliders, to the common potential point. The galvanometers are both interposed between such resistances, and the common potential'p'o'int.

For certain purposes. such as, resolution or subtraction, a reversing switch is interposed in the connections to the magnitude potentiometer for one or more of the given vectors, that is, it is desirable or necessary to, in effect, combine, a vector, which is a positive vector, as a negative vector. This is easily accomplished by inserting the reversing switch in the leads to the terminals of the magnitude potentiometer, or between the magnitude potentiometer and the angle poten tiometer.

If a galvanometer is used to indicate zero current flow, it is desirable to provide a means for readily cutting off current flow when it is believed a balance is obtained. By breaking and making the circuit, a slight departure from zero reading is more readily apparent. Applicant prefers a simple push button switch for this purpose.

It is well understood that a'plurality of vectors may. be combined by combining two and then combining the resultant with another and so on, so a machine presenting the necessary parts to set up two vectors and ascertain their resultant is generally ample, but it must be understood that parts may be provided to set up any number of vectors simultaneously and secure their resultant. To do this, is merely necessary to add such duplicate parts as are necessary to set up the given vectors.

Various arrangements may be made embodying the principles underlying applicants invention but for purposes of illustration applicant has herein illustrated an explanatory construction and a particular preferred physical embodiment.

In describing the invention in detail, reference will be had to the accompanying drawings and the several views thereon, in which like characters of reference refer to like parts throughout the several views and in which:

Figure 1 is aschematic view of an arrangement embodying th in ention; Fig. 2 is a View showing given vectors and their resultant obtained by composition; Fig. 3 is a view similar to Fig. 2, but showing a resolution of vectors; Fig. 4 is a schematic view of a preferred embodiment of the invention; Fig. 5 is a detail view particularly illustrating cams and closely associated parts used in the practice of the invention; Fig. 6 is a crosssectional view, illustrating the manually manipulatable parts of an angle potentiometer and may be considered as a cross-section on the plane indicated by the line VIVI of Fig. 4; Fig. 7 is a schematic view of a modified form of angle potentiometer.

The arrangement of apparatus schematically or diagrammatically illustrated by Fig. 1 shows, what might be considered, an elementary construction, especially suitable for disclosing the principles of the invention.

cooperating-with resistance 12, and the other,

l5, cooperating withresistance l3. Both sliders are rigidly connected to and 'move synchronous- 1y Witha' common shaft l6 which is intended to-bemanually'operated. The amount of angular '"nio'vement of shaft 16' maybeindlcatedin any usual or-desired' manner as by" afiixingpoi'riter arm thereto'which' cooperates-with a suitable fixed scale l8. Each -'divi'sion"o f the'scale, as '18, may be considered as corresponding to-any "desired 'inagnitude, as a length, aforceyor a weight, expressed in'anyunits.

"Each angle potentiometer, such'as fi, 6 and"-'|,

I includes an" elbngated resistance,- asiS, and two Each slid'er is pivoted near 'one' end, as at 22.

' conductor. 'a common'connection, as 3|,

sliders moving the'reover, one 2|] andthe other 21. A cam is providedfor each slider, as cam '2'4 for slider to, and cam 2s for slider 2|. Thecams are mounted on a common shaft 26 which-may be provided with a pointer arm 2'1 moving over a fixed scale 28 for the purpose of indicating the relative rotation or angular position of sh'aft 26 and so of the cams 24 and 25 and so the positions of the arms 20 and 2|. V

Each of the magnitude potehtiometers as 2, 3' andAQhas'the adjacent ends, at one end of the resistance 12 and [3, connected together, asby conductor 29 and-by conductor 30, to a common This common conductor connects to connected to 'the center of each of the angle potentiometer resistances, as 19. This common conductor also corinects to one side, as 32, of galvancmeter 8 and one side,as 33, of galvanometer 9. The object of'this connection is to cause all of the'points so connected to be as near, as it is possible to 'm'akethese points, of the same potential.

'One'side, 34, of'the source of potential I, through the switch 10 and through the reversing switch ll connects the free end of resistance 12 of magnitude potentiometer 4, through conductor 36, and the other side, 35, of the source of.

8, .although the connections to potentiometer 2 are reversed relatively to those of potentiometers 3 and 4 for reasons to be hereinafter disclosed.

Each of the sliders, such as l4 and i5, is connected, as by conductors 38 and 39, respectively, to the free ends of angle potentiometer resistance l9.

By the arrangement as hereinbefore described,

the positions of sliders l4 and I5 relative to resistances l2 and [3 determine the magnitude of the potential at the free ends of an angle potentiometer resistance, as l8. The magnitude potentiometers as 2, 3 and 4 are so constructed that in any given position of the sliders, as l4 and I 5, the potential applied to conductors, as 38 and 39 shall be equal. The construction of resistances, as I9, of the angle potentiometers as 5, B and l is such that when equal potentials are applied to conductors, as 38 and 39, there will be an equal potential drop between each free end of a resistance, as 19, and its common connection 3|.

The cams 24 and 25 are given a form such that the motion of the arms 20 and 2| over a resistance, as 18, is in accordance with a simple harmonic motion but one arm, due to the cams, is displaced, in eifect 90 angular degrees from the other so that one arm may represent the sine value and the other the cosine value of a particle moving with a simple harmonic motion, that is, one represents the sine value of the angle of movement and the other the cosine value.

The angle potentiometer constructed and operating as described will, therefore, produce at a conductor, as 40, a potential corresponding to, say the sine value of an angle and in conductor 4!, a potential corresponding to the cosine value of the same angle. The conductor 40 being connected to galvanometer 8 will produce a deflection of the pointer and the potential of conductor 4| bein connected to galvanometer 9 will produce adeflec tion in the pointer of that galvanometer.

It is to be noted, that in Fig. 1 resistances 42 and 48 have been interposed in the conductors 40 and 4| between those conductors and the galvanometers 8 and 9 respectively, and that similar.resistances have been insertedin the similar conductors from the other angle potentiometers. The object of inserting these resistances is to have the galvanometer act as a potential instrument with a minimum disturbance of the potential due to current flow. The galvanometer is really used as that class of instrument which indicates a desired result when it indicates zero, that is, when no current flows.

The several magnitude potentiometers illustrated in Fig, l, by known methods thoroughly well understood by those skilled in the electrical art and so unnecessary to be described herein, may be adjusted so that a pointer, as ll, of a potentiometer at the various positions of the scale l8 will apply equal potentials to both conductors as 38 and 39. Further, the several magnitude potentiometers may be adjusted so that a given angular movement of each will impose the same value of potential on each of the conductors connected thereto, as 38 and 39.

In the same way, each of the angle potentiom- ,eters 5, 6 and I may be so adjusted that when a pointer, as 21, is at a given position relative to a scale as, 28, definite potentials will be applied to conductors 40 and 4|, one connecting to galvanometer 8 and the other connecting to galvanometer 9 and the same relative positioning of the corresponding pointers on the other angle potenlems, that ometer 4 would be tiometers will apply the same potentials to the same galvanometers, for the same position of magnitude potentiometers 2,3 and 4.

The resistances, as 42 and 43, are equal. From the lower terminal of 8 there are four paths, one through the meter and through each resistance. The voltages applied to the resistances cause currents therethrough and perhaps also through the meter. The algebraic sum of currents is zero by Kirchofis law. The voltage applied by 5 is adjusted until the current through 42 causes the algebraic sum of the currents through the three resistors to be equal, algebraically, to zero when there will be no current in the meter. Then as the resistances are equal and may be considered as of unitary value the algebraic sum of the voltage drops in the resistors are equal to Zero. Since the voltage drops are the voltages tapped off by the wipers, as 20, these are algebraically equal to zero also.

The several pieces of apparatus arranged as shown in Fig. 1 may be used to solve vector probis, by its use a resultant may be obtained as an addition or composition of vectors or as a subtraction or resolution of vectors.

In Fig. 2, a vector A and a vector B are shown. The vector A is at an angle of ten degrees to the reference line O-O and the vector B is at an angle of seventy degrees to the same reference line 0-0. It is desired to ascertain the magnitude of the resultant of these two vectors and its angle to the same reference line 0-0. In order to do this, the pointer I! of magnitude potentimoved over the scale 18 a certain number of divisions corresponding to the magnitude of the vector, say the length of the vector A. Then the pointer 27 would be moved ten degrees from the zero of the scale 28 to indicate the angle of the vector A to the reference line 0-0. As the resultant of vector A and B is to be obtained by addition, the reversing switch I I would be in the position as shown in Fig. 1. With reversing switch H in that position, the pointer on magnitude potentiometer 3, corresponding to the pointer l1, would be moved over its scale an amount corresponding to the length of vector B and then the angle potentiometer 8 would have its pointer, corresponding to pointer 21, moved through an angle of seventy degrees from the Zero point corresponding to the angle of the vector B to the reference line OO. Under the conditions specified, the potentials applied to angle potentiometers 8 and 1 would be additive. In order to obtain the resultant, the pointer of magnitude potentiometer 2, corresponding to pointer l1, would be moved over its scale a greater or less amount and the pointer of angle potentiometer 5 would be moved over its scale a greater or less amount until, by trial and error, positions for each would be found which would bring both pointers of 8 and 9 to the mid position. Potentiometer 2 would then be read, giving a length, and potentiometer 5 would be read, giving an angle. The length of the resultant of vector A and vector B would be the length C and the angle would be the angle of the resultant to the reference line O-O and would lie as shown by line C.

ing an; angle.

4 -'order renews are ivtidindfiiitch '1 l ls'thrown to "the lower iidsitlbn. as viewed-mi ls.- 1. jI-fhe pointer l'l of'magnituile'?potehtlctneter' t'is then moved" over *the scdlv We. certain number of divisions commas to the-magnitude ofthe zero-of the "scale E8 to indicate the-angle OI fthe vector D to the rerer'ence 'line 'I'h'eri-the pointer "on fiiagndtude' potentiometer 3; corresponding to the'boihten -I1-would-"be-'movedover scale an"amountcorresponding to the'length of vector E andth'enthe potentiometer F'would "have itsp'inter correspondingto pointer "21 "movd throi'igh strangle F 80 degrees frenifthe zero 'p'oint correspondingwo the'angle 'of the vector to the reference-line 0--0. Under'the conditions 'speoifid'the' potential applied to' be'th angle potentiometers' G-a'nd- T'would be subtractive. In order to obtain the resultant, the pointer '20 "of magnitude potentiometer: 2 corresponding to the pointer I"| would -be-mdved "over its scale a g'reateror'lessf amount and 'the pointer' -of angle "potentiometer swans be'moved over-dts'soale a greater or less amountuntil; by trial and error, positions for each would found which would brihg'bdth'pointers of8-and'9 to the mid positlon. "Potentiometer ftvould'then bereadglving a length and-potentiometer would be read giv- The length "of the resultant of vector '13 minus vector-D wouid be the length F and the anglewouid bethe angle of {the resultant to the reference line 0-0 and would lie as shown "by line F. It is' again to 'be observed that the resultant potential was o posite in polarity to that of E.

Although in Fig. 1, there have beenshown means for adding 'or subtracting two'vector and obtaining "the res ltant; and althoifgh-the' specific examples, as illustrated by Figs. 2' and 3. include two vectors only and the resultanflthereof} it must be understood that 'the illustratlonand the specific examples are -onlyillustrative of a principle. This principle; physical-embodiment,

may include a resultant 'angle'fiotehtiorneterhnd "magnitude 'potentiomter 'and any number" of separate vector magnitude potentiometers and "angle potehtioni'eters. Furthen-althougn'fig. 1

illustrates a reversing switch I Pin the connections to" one magnitude'potentiometer o'nlyiit-is to be understood that this isn ierely-illustrative and the same underlying principle-may beinore fully embodied "by including sueh reversing "switch in the leads to themagriitude' potenageetiaea.

edge-oi particular materiala-and-the known skills "of engineers and scientistsare' tobe availed of Anorder-to have. as a, result, an assemblage which "will give the result desired withthehighest pre- 5 "onion" possible orthatis consldereddeslm'ble and which 'w'ill' be subject tothe minimum amount of mechanical and electrical defectsand troubles.

--'Although "the illustration; Fig.- 1 3 *is of" an" arrangemen-t which-is entirely practicable-andwne in i 4451s aud ts 'eacli-xlsignates a ddetle magnitude potentiometer ooiistnieted ar- "ranged,- and -iun'ctlonmg exaet ly' like the niagniitl'ide notentiomter' irr' l igi 1.-

l l'n Fig-1 4; there is" a-double noleg donble'thrbw switch 41, 'eonstruetedxarranged: and 'fimctioning exactly like the d8ifl'5le "1ole doul9le 'throw reversing switch- H- of 1. 4

J In Fig. 4, there are 'two' 'galvanemetersi fl and I 19-, constructed. arranged; and functioning exa'ctly like the twcP galvanometers' 8 and 9 of Fig; 1'.

In Fig. 4; there is" BISOHPCG bf potential-wand a mainline switch 51 geaeh eonstructed}-arfanged,

so. and functioning exactly likethe sourcemf po- :zs'Fig: 1. In addition, there'is an-angle potentiometer 54; having no movable manually adjustable parts, which eo'rresponds -to'and' takes the place of the angle potentiometer Po'f'Fig. 1. r'eason- 'applican't employs the "'device -54 ,f--which-"is 4 what might be called afixed angle'potentiometer,

is because it is'bossible-andless' expensive. It is possible; because any two 'vectorsmay becbm sitlered asreferred-to "any givenba'se line-with "which th'ey may make angles. In'factmneol the '45 vectors may be 'c'OnS l'de'Id' as 'coincidingwitli the line. Thisis-just what applicant'takes'advantage of in-"using' lnsvectorcalculator;'aswill hereinafter 'n'i'ore fnlly'apbear; 'soth'at one ofthe vectors may be' considered zero angle unn cessaquently',- no manually adjustableanglepotentiometer is'necessaryupon whiclrto' set up'its angle. It is merelynecessary to 's et'jupits magnitude "on "a magnitudepotentlometer. It'wili be noted that connection from fixed anglehotentiometenfl is tiometers "in twoormore cases. -"-In'- short,-""the' made at only one end by awire 58'tocos'ine'.gal-

"principle exemplified by Fig: 1, and the 'ex'ambles given are-merely illhstrative of the factth'at liwo given vector and the resii1tant"sl'iown br-"-any "hui'nber of vectors may be added and any mim- "ber 'of vectors subtracted therefr'om and the "re- *sdlt'ant shown. It is xnerely-necessary' to have the maximum then the center tap becomes the one magnitude riotentiometer-and one ang p tent'iom'eterfor each vector quantity and as inany reversing switches such as -I l,-as thereare vectors 'to be subtracted, and in addition a re- "sult'ant' magnitude potentiometer and angle p0- ten'tiometer.

the arrangement as shown in Fig. I'andin con- =van-ometer l9 and there is no connection from the other endorse to sine galvanolneter I8. The missing conductor 'could besilppli'ed', but it isunnecessary because regardless of themagnitflde'of "may be added and the resultant shown: cra odpotential supplled'bymagnitudepotentiometeffi, 'number of vectors may be subtracted -from a the end 51' would always'be at a maximum :potential in reference to common; and end- 58"wduld be ata mlnmum 'poteritial'in reference to comnfon, that is, whenthe cosine'end 5T'is considered sine or O, and as the potential'ln'refe'rence to the common is O at the center 'tap,it is of no utility to connect it through the galvanometer to common, 'asit'would have no effect whatsoever.

7 In Fig. 5, a detail of the cams and mounting,

as used in the devices of both Figs. 1 and 4, is shown. The cams, as 24 and 25, are mounted on the sleeve 12' which in turn is mounted rotatively on shaft 58mins fully'shown in Fig. 6. The slider "necting the various'parts, that all of the knowl-' arms 20 and 2| are each pivoted, as at 22 and each arm carrie a pin as, I09 and I04, which bears against the periphery of a cam. Each slider arm is held in contact with its cam by any suitable means, as a spring attached to any suitable stationary point. It is preferred to have the actual contacting points of the sliders made of a special metal and so the actual slider tips I06 and I01, are fastened in any suitable or appropriate manner, as by screws, I08 and I09, to arms 20 and 2|, respectively.

In the device of Fig. 4, instead of having three separate pointers, as 21, one on each shaft, carrying cams, a column, as shown in detail in Fig. 6, is provided, including all of the movable elements for imparting motion to the cams and cam shafts.

In Fig. 6, 56 and 51 designate stationary plates or frame members and 55 a top panel. 58a designates a central shaft. At 59 is a sleeve fastened to shaft 58a in any suitable or appropriate manner, as by a pin 60. The sleeve 59 has a shoulder and a screw threaded portion 62. One pair of cams 63 and 64 is mounted on the sleeve abutting the shoulder 6| and are therefore positioned and are held therein by the washer 65 and lockwasher 66 and the internally screw threaded collar 61. The collar bears on an anti-friction wear washer 68 resting on the frame 51 and the lower end of the sleeve 59 resting in a centralizing or positioning orifice 69 of the frame 51. the sleeve 59 is an anti-friction or wear washer 13a resting on the sleeve 59 and thereabove is a flat spring 1I, tensioned between the washer and the frame 56.

Above the frame 56, there is an elongated sleeve 12 which extends from a bearing cavity 13 in the frame 56 toward the upper end of the shaft. This sleeve 12 may remain stationary while shaft 58a turns, as will appear more fully hereinafter. This elongated sleeve 12 carries th pair of earns 15 and 16. One, 15, is in the formshown integral therewith; the other, 18, is secured thereto by abuttin shoulder 11 and being held in place by washer 18, backed by lock washer 19 and internally screw threaded collar 80, threaded on to the screw threaded end 8I of the sleeve 12. The sleeve, and so the shaft, is positioned longitudinally by bearing at the lower end in the cavity 13 of the frame 56 and by having a shoulder 82 abut 2. depending boss 83 of the frame 55.

Above the frame 55 there is first positioned a sprin washer 84, tensioned between the upper face of the frame 55 and the lower face of a split boss 85, which boss is rigidly attached to the elongated sleeVe 12 by any suitable means, as screws passed through the orifices 86 and 81. The split boss is preferably integral with arm 88.

Above the arm 88 there is a graduated dial 89 held in place by a washer 90, which in turn is held in place by suitable means, as an annular helical spring 9| which seats in a groove 92 of a collar 93 integral with 88. The dial 89 may be rotated independently of the arm 88 by reason of the construction described.

Above collar 93 and resting thereon is the flange 94 of a sleeve 95. This sleeve surrounds sleeve 12. Just above the flange 94 and having its hub surroundin the sleeve 93 is a pointer 96. The pointer is spring pressed to the flange by flat spring 91 which abuts a washer 98, abutting a finger terminal 99. This finger terminal 99 surrounds sleeve 95 and also sleeve 12, but sleeve 12 is terminated at about the point I00, so that finger terminal 99 may be fastened to shaft 58, as by set screw 14, without at the same time, fastening shaft 58 and sleeve 12 together because, as

Above will hereinafter appear, at times, it is desired to rotate shaft 58 without rotating sleeve 12.

By the construction just described, as shown in Fig. 6; earns 63 and 64 may be rotated by finger terminal 99 without rotating cams 15 and 16; dial 89 may be rotated independently of arm 88; and pointer 96 may be rotated while all other parts are held stationary; and a rotative movement oi arm 88 will rotate cams 15 and 16.

In Fig. 4. the pointer 96, dial 99, 88, sleeve ?2, and shaft 58a are shown, as arranged in Fig. 6. and, in addition, a fixed line I0! is shown. hi line is so positioned that if line I02 on arm 88 is caused to coincide therewith, the cams 15 and 16 are at what might be called their zero position. That is, the angle potentiometer 52 is in such position that the potential representative of the sine is a minimum and that for the cosine is a maximum, or vice-versa. If then pointer 96 is brought to lin IN, and shaft 50a correspondingly moved, earns 63 and 64 are likewise at their zero position.

If one has given vectors to solve, by addition, say the vectors of Fig. 2, the angle I0 of vector A could be substracted from the angle 70 degrees of vector B giving 60 degrees as a difference. This difference of 60 degrees would be the amount by which arm 88 should be moved, in degrees, from the fixed zero IN. This could be easily done by having the zero of dial scale 89 coincide with IM and moving arm 88 until line I02 coincided with 60 degree line on the dial, then there would be an effective angle of 60 degrees between the positions of fixed potentiometer 54 and movable angle potentiometer 52. Then, by retaining this setting and manipulating magnitude potentiometer 44 and finger terminal 99, thus rotating shaft 58 and cams 63 and 64 only, a balance could be obtained at galvanometers 48 and 49 just as a balance was obtained in the case of galvanometer 8 and 9. The balanced position would place pointer 96 opposite a certain angle value on dial 89. This angle value, thus obtained, would be the angle of the resultant C from the vector B.

A better way to use the device, however, which avoids all mental mathematical operations, would be to first set dial 89 with the 10 degree mark coinciding with line I02 of arm 88, this would, in effect, make the B vector the reference line, then both dial 89 and arm 88 would be rotated together until the '70 degree mark on the dial coincides with the zero mark I M. Thereafter, proceed as before. The angular value denoted by the position of pointer 96 would then indicate the angle of the resultant C from reference line 0-0 of Fig. 2.

Applicants invention is of especial value in problems encountered in dynamic balancing of machines. Such problems have special features therein and applicants preferred device has been so arranged that it may be most readily used in connection with such problems. A typical example is the balancing of a rotating body. It is well known that an unbalancing weight may cause disturbances which are out of the plane through the axis of the rotating body and the unbalancin weight. In some cases as much as degrees around the axi displaced therefrom, and is generally referred to as the high spot" which is not necessarily, as stated, in the plane of the axis and the unbalancing weight. It is, however, desirable for pointer 96 to indicate directly the angle of the point where a balance weight should be placed, when solving vectors in balancing. This is accomplished by first ascertaining, by suitable methods well known in the art, the vibration amplitude and angle of the unbalance in a given machine. Then a test weight is applied to the machine and amplitude and angle again determined. If the vectors, which we may call A and B respectively, are subtracted, a vector, which we may call C is obtained. This vector represents, in one sense, an angular position of pointer 96. But pointer 96 indicates, not

the position of the weight but the position of the resultant of the original unbalance and the test weight, consequently, after the angle of vector C is ascertained by pointer 96, the finger terminal 99 is held and pointer 96, swung around until it indicates the angular position of the test weight. So, while the finger piece, and so the cam, indicate angular position of the resultant, the pointer indicates the angular position of weight which participated in causing it, and so if vector C is now balanced against original vector A, omitting vector B, the pointer will then indicate the angular position where a weight should be placed to correct the unbalance. It, of course, is under stood, that the magnitude of the weight is ascertained from a reading of the magnitude potentiometer. The just above described operation would result in getting pointer 96, out of step,

with finger piece 99 and so out of step with the cams. To provide for this, there is a suitable means such as a mark I i on the finger piece and a mark II I on the pointer 96. When these marks coincide, the parts are in proper relative position or in step.

The device of Fig. 7 is an alternative for an angle potentiometer.

In Fig. 7, there is shown a form I I2 upon which resistance wire comparable to the resistance wire I9 of Fig. 1 is wound.- The form .I I2 is such that the wire wound thereon as regards the several turns has resistance which varies as-the ordinates of a curve of simple harmonic motion. Sliders as H3 and H4 are insulatingly mounted on a shaft I I5, corresponding to cam shaft 26 of Fig. 1. Taps at H6 and II! connected together, at the two longest turns correspond to the wire 3| of Fig. 1 and taps II 8 and- H9 at the two shortest turns correspond to the wires 38 and 39 of Fig. 1. Wires I20 and I2I, corresponding with wires 40 and II of Fig. 1, connect with brushes I22 and I23 which electrically-connect by means of sleeves with sliders H3 and -I I4 respectively, which are 90 degrees apart,

The device takes the-place of the angle potentiometers of Figs. 1 and 4.

Although the invention has been described as applied to simple vectors and to vectors as used in dynamic balancing, it is to be understoodthat the-invention and the devices described are applicable to many other'situations,such-as triangulation, navigation, direction finding and gunfire control.

It is further to be understood, that although the invention has been described as though the physical embodiment were a closely placed compact device, nevertheless, each and every one of the angle potentiometers and the magnitude potenti'ometers may be remotely positioned one to the other.

Although I have particularly described several particular embodiments of my invention and explained the principle, construction and mode of operation thereof, nevertheless, I desire to have it understood that the forms selected are merely illustrative but do not exhaustthe possible physical embodiments of the idea of means underlying my invention.

What I claim as new and desire to secure by Letters Patent oi the United States, is:

1. An apparatus for combining vectors including, in combination: a source of potential; a plurality of magnitude potentiometer windings, the terminals of each of said potentiometers being connected in multiple with said source; a reversing switch interposed in the circuit of one of said potentiometer windings; a plurality of sliders, a pair cooperating with each potentiometer windin ,-the sliders of each pair being in contact with the cooperating winding at points of equal potential by opposite polarity; means to move each one of each pair in unison to maintain the condition of equal potential but opposite polarity contact; a plurality of angle potentiometer windings, the terminals of each winding. being connected, respectively, one to one slider of a pair and-the other to the other slider of a pair; two cams associated with each angle potentiometer except one, said cams mounted in pairs for rotation and the cam of each pair. positioned rotatively degrees apart; a plurality of sine sliders and of cosine sliders, one of each cooperating with each angle potentiometer winding, the .cams positioned for causing the sine and cosine sliders to .sweep over and in contact with their angle potentiometer winding so that when the sine slider is at a maximum potential point, thecosineslider being at a minimum potential-point and the motion of each being a simple harmonic motion; means connecting the exact one. half potential point of each magnitude potentiometer winding and the exact one half potential point of each angle potentiometer a connection point,

means including a resistor separately connecting each sine slider to said connection. point; a galvanometer connected between the connection point and the means connecting the .half .poten-.

tial points; asecond connection -.point, means including a resistor separately connectingeach.

cosine slider to said connection point; a galvae nometer connected between the .connection. point and the means connecting the half .potentiaL points; a connection from one endof .theangle.

potentiometer without-sliders to one of the gals vanometer terminals whereby when .a balanced indication is given by the galvanometers the settings of the various sliders represent vectorvalues andangles and the resultant and its angle.

2. An apparatus for combining vectors, including,.in combination two galvanometers; means including a potentiometer winding having its one half potential point connected .to one. side of one of the said galvanometers and .one end.

permanently connected to the other side of.the

said-galvanometer for applying a potential-to the said one of the galvanometers representative of one of the sine-cosine functions -.of the angle of a vector of assumed angular position. wherein the function is a maximum and the. complementary function is a minimum; potentiometer means including a I resistance,.

for simultaneously determining balancing potentials for such galvanometers in terms of the angle and magnitude of a resultant vector.

3. An apparatus for combining vectors; including, in combination: a potentiometer winding;

' two sliders making connection with the potentiometer winding; one slider positioned relative to the winding representative of the sine value of the angle of a vector, the other slider positioned relative to the winding representative of the cosine value of the same angle; means for simultaneously so moving said sliders that in any moved position one is still representative of the sine value of an angle and the other is representative of the cosine value of the same angle; a sine galvanometer and a cosine galvanometer; a source of potential; connections between the source, the galvanometers, the potentiometer winding and the sliders whereby potentials derived by the sliders are applied to the respective galvanometers; potentiometer means for applying to said potentiometer winding a voltage proportional to the magnitude of said vector; means for applying a potential to one of the galvanometers representative of one of the sine-cosine functions of the angles of a second vector, asecond potentiometer means for applying to said potential applying means a voltage proportional to the magnitude of said second vector, said second vector having an assumed angular position wherein the function is a maximum and the complementary function is a minimum includin a fixed potentiometer winding having its middle point permanently connected to one side of the said one galvanometer and one end permanently connected to the other side of the same galvan-ometer; means to apply potentials to the galvanometers algebraically equal to the algebraic sum of the potentials applied representative of the two angles and interconnected means for indicating the value of the angle of a vector corresponding to the last mentioned potentials and its magnitude.

4. In a vector calculator, including, in combination: a plurality of potentiometers; each potentiometer having means for applying thereto a voltage proportional to the magnitude of a vector; a pair of sine and cosine sliders for each potentiometer for deriving from the potentiometer potential values equivalent to sine and cosine values of given vectors; a cam for operating each slider; a shaft; a pair of sine and cosine cams attached to the shaft; a sleeve on the shaft adapted to rotate independently on the shaft; an arm bearing an indicating line attached to the sleeve whereby the sleeve may be rotated independently of the shaft; a pair of sine and cosine cams attached to the sleeve; a graduated dial surrounding the sleeve and rotatable independently Of the arm and the sleeve; a second sleeve surrounding the first sleeve and projecting therebeyond, said sleeve formed with a flange; a pointer extending over the dial and formed with a hub surrounding the second sleeve and resting on the upper side of the flange; a finger piece surrounding the second sleeve and attached to the shaft; a spring washer between the lower end of the finger piece and the pointer whereby the pointer may be moved independently of the finger piece but normally moves with it; said pointer provided with an indicating mark and said finger piece provided with an indicating mark whereby both may be brought into registry; a fixed mark adjacent the end of the arm and the periphery of the dial, whereby when the Zero of the dial, the indicating mark of the arm and the pointer with its indicating mark in register with the indicating mark of the finger piece are all in register with the fixed indicating mark all cams are in a known position and relation one to the others and the sine sliders and cosine sliders are in a position deriving potentials as for a zero angle; a sine galvanometer and a cosine galvanometer, a source of potential; connections between the source, the galvanometer, the potentiometers and the sliders whereby potentials derived by the sliders are applied to the respective galvanometers; means for applying a potential to one of the galvanometers representative of one of the sine-cosine functions of a vector of assumed angular position with relation to the fixed mark wherein the function is a maximum and the complementary function is a minimum including a fixed potentiometer winding having its middle point permanently connected to one side of the said one galvanometer and one end permanently connected to the other side of the same galvanometer; means for applying to said fixed potentiometer a voltage proportional to the magnitude of said last named vector the said first-mentioned connection being such that the potentials derived from one potentiometer by one pair of sine and cosine sliders being opposite in polarity to that derived from at least one of the other potentiometers.

PETER DAVEY. 

